MAYBE

Problem:
 g(s(x),s(y)) ->
 if(and(f(s(x)),f(s(y))),t(g(k(minus(m(x,y),n(x,y)),s(s(0()))),k(n(s(x),s(y)),s(s(0()))))),
    g(minus(m(x,y),n(x,y)),n(s(x),s(y))))
 n(0(),y) -> 0()
 n(x,0()) -> 0()
 n(s(x),s(y)) -> s(n(x,y))
 m(0(),y) -> y
 m(x,0()) -> x
 m(s(x),s(y)) -> s(m(x,y))
 k(0(),s(y)) -> 0()
 k(s(x),s(y)) -> s(k(minus(x,y),s(y)))
 t(x) -> p(x,x)
 p(s(x),s(y)) -> s(s(p(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))))
 p(s(x),x) -> p(if(gt(x,x),id(x),id(x)),s(x))
 p(0(),y) -> y
 p(id(x),s(y)) -> s(p(x,if(gt(s(y),y),y,s(y))))
 minus(x,0()) -> x
 minus(s(x),s(y)) -> minus(x,y)
 id(x) -> x
 if(true(),x,y) -> x
 if(false(),x,y) -> y
 not(x) -> if(x,false(),true())
 and(x,false()) -> false()
 and(true(),true()) -> true()
 f(0()) -> true()
 f(s(x)) -> h(x)
 h(0()) -> false()
 h(s(x)) -> f(x)
 gt(s(x),0()) -> true()
 gt(0(),y) -> false()
 gt(s(x),s(y)) -> gt(x,y)

Proof:
 Open